If you talk to Lucy, she'll tell you that she needs the drug Buffout (which can be obtained by looting or buying from various dealers) to treat the Rickets, a condition that has to do with the softening of bones, and can cause fracturing. This leads to her explaining Cave Fungus, vegetation that is native to the caverns and thrives on Strange Meat. If you give Lucy 3 buffouts she'll give you one unit of Cave Fungus.

Alternatively the player can talk to Eclair, the owner of a store or "restaurant" in Little Lamplight, and ask him about the fungus. He tells you that he needs more Strange Meat (human flesh), and that this meat makes up the majority of the kids diet here. The player can give 3 pieces of Strange Meat to him for one unit of Cave Fungus.

However before this can all be done the player has to get Mayor MacCreadys approval. The player can convince him to let you trade with either one of the kids in dialogue. You can pass a speech check, use barter, or if you have the Child at Heart perk a new dialogue option will appear. Once this is done you can begin trading.